Rayleigh quotient minimization method for symmetric eigenvalue problems

被引：0

作者：

Miao, Cun-Qiang ^{[1
]}

Liu, Hao ^{[2
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Coll Sci, Nanjing 210016, Jiangsu, Peoples R China

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2019年 / 38卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Eigenvalue; Eigenvector; Rayleigh quotient; Convergence analysis; Newton method; LOCAL QUADRATIC CONVERGENCE; STEEPEST DESCENT METHOD; JACOBI-DAVIDSON; LANCZOS-ALGORITHM; ITERATION; EIGENPAIRS; VECTORS;

D O I：

10.1007/s40314-019-0962-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a new method, which is referred to as the Rayleigh quotient minimization method, for computing one extreme eigenpair of symmetric matrices. This method converges globally and attains cubic convergence rate locally. In addition, inexact implementations and its numerical stability of the Rayleigh quotient minimization method are explored. Finally, we use numerical experiments to demonstrate the convergence properties and show the competitiveness of the new method for solving symmetric eigenvalue problems.

引用

页数：16

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